This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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18
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2answers
810 views

Did Zariski really define the Zariski topology on the prime spectrum of a ring?

The question is not: “Did Zariski really define the Zariski topology?” It is: “Did Zariski really define the Zariski topology on the prime spectrum of a ring?” Here is the motivation. --- On page ...
1
vote
1answer
647 views

Books on improving mathematical problem solving generally and in an exam setting

looking at recommendations for books for people like me who are not mathematics naturals. have been through polya's 'how to solve it' and noticed that i did not pick up those heuristics naturally ...
2
votes
2answers
281 views

Reference request: group theory

Currently I'm studying differential geometry and PDEs - so I often meet the use of groups. I also studied symmetries methods for solutions of differential equations but the connection between Lie ...
4
votes
0answers
76 views

References about the symmetric products of a stack

I would like to know references about a construction of the symmetric product (or the moduli space of effective divisors) $X^{(d)}$ of a stack $X$. I am currently thinking about the following case: ...
4
votes
1answer
309 views

Bounds on roots of polynomials

What bound is there on the roots of a given polynomial, in terms of its degree and coefficients? Consider the polynomial $p(x) = 3x^7 – 5x^3 + 42$. Would you not agree, without doing any calculation, ...
5
votes
3answers
606 views

Applications of descriptive set theory to mathematical logic?

The Wikipedia article Descriptive Set Theory asserts it has applications to logic, but gives no examples. Kechris' text Classical Descriptive Set Theory does not discuss logical applications, judging ...
0
votes
1answer
261 views

Where can I find specific Jacobi determinants in the Bronstein-Semendjajew reference work?

I'm trying to find the fact that the Jacobi determinant (functional determinant) of the cartesian->spherical coordinate change is $r^2 \sin\theta$ in a mathematical reference book, "Taschenbuch der ...
19
votes
7answers
22k views

Good abstract algebra books for self study

Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, ...
6
votes
8answers
492 views

Books or site/guides about calculations by hand and mental tricks?

Any ideas about books I can get, from amazon? I need to get really good at mental math and math by hand because I'm taking an exam soon and that without a calculator. Thanks.
50
votes
2answers
4k views

Sheaf cohomology: what is it and where can I learn it?

As I understand it, sheaf cohomology is now an indispensable tool in algebraic geometry, but was originally developed to solve problems in algebraic topology. I have two questions about the matter. ...
7
votes
1answer
2k views

Restricted Three-Body Problem

The movement of a spacecraft between Earth and the Moon is an example of the infamous Three Body Problem. It is said that a general analytical solution for TBP is not known because of the complexity ...
7
votes
1answer
142 views

Bounds on the gaps in a variant of polylog-smooth numbers.

Sorry for the long intro. I think the explanation motivates the question and puts it in context. But if you want to skip the story, then just move on to the grey boxes; they should contain enough ...
5
votes
4answers
813 views

Group theory text [duplicate]

Possible Duplicate: Introductory Group theory textbook I am an Indian student currently in the eleventh grade.I haven't yet learned calculus(I am learning it ) but I would also like to ...
6
votes
2answers
373 views

The Néron-Tate canonical height on elliptic curves

I have been trying to understand the Néron-Tate global canonical height of algebraic points on elliptic curves. Let $K$ be a number field, $E$ an elliptic curve (over $\mathbb{Q}$, say), and $E(K)$ ...
4
votes
1answer
366 views

Looking for an “arrows-only” intro to category theory

I have often seen it remarked in passing that the "collection of objects" that appears in the standard definition of a category is, strictly speaking, superfluous, and that it is possible to give an ...
14
votes
3answers
917 views

Looking for student's guide to diagram chasing

I'm teaching myself some category theory, and I find that I'm very slow with diagram chasing. It takes me some times a very long time to decide whether adding an arrow to a diagram preserves the ...
2
votes
0answers
187 views

Topology of pseudo projective space

I don't know if "pseudo projective space" is a general accepted term, but I once read a book on general topology where the term was used for $\mathbb{S}^n / (\mathbb{Z}/m\mathbb{Z})$ (where you get ...
1
vote
2answers
123 views

Reference Request: Greatest Even (Odd) Integer function

This probably isn't the most important question, but I'm working on something where I've found it convenient to define the following two functions (on the integers): $$ I_o(q):= \begin{cases} q ...
7
votes
1answer
516 views

Do there exist any visual representations of prime factorizations?

Introduction: The question that I really want to ask is, “Are there any well-known visual representations for the integers $\ge 2$, with perhaps one of them even being regarded as canonical?” However, ...
1
vote
2answers
101 views

Displaying a reduction of inequalities

This question is about style and typesetting, but I believe it is more appropriate for this site than a TeX site. When a bound is being established for some expression, it is not uncommon to see ...
7
votes
3answers
355 views

Does this class of cipher have a name? What weaknesses does it have?

Some Background In October I have been asked by the school I teach at to organise and lead 'a hands-on cryptography session' for a bright group of 13 year olds to follow a talk on Enigma by an ...
1
vote
0answers
247 views

What is a Zariski closure? [duplicate]

Possible Duplicate: Reference for Algebraic Geometry I'm rather clueless about this exercise. What is a Zariski closure? What topics/books should I read on to gain some knowledge on solving ...
2
votes
1answer
123 views

Regularity ascends from a Noetherian ring to a polynomial or power series ring over it

I am looking for a proof of the following statement: A Noetherian ring $R$ is regular if and only if $R[x]$ is regular if and only if $R[[x]]$ is regular. I am trying to understand the properties ...
11
votes
3answers
1k views

Exercises on Galois Theory

I need a source for exercises on classical Galois Theory, or to be more specific, Galois extensions of finite fields and the rationals as well as applications (solvability by radicals, for example). ...
18
votes
3answers
2k views

What is the origin of the expression “Yoneda Lemma”?

Thank you very much in advance for telling where the expression “Yoneda Lemma” comes from. EDIT 1. On page -14 of Reprints in Theory and Applications of Categories, No. 3, 2003. Abelian Categories, ...
7
votes
1answer
205 views

Fixed point: sets and measures

Let $X$ be a Borel space with a Borel measure $\mu$. Suppose $\xi: X\times X\to\mathbb R_{\geq 0}$ is a continuous function and put $s(x) = \{y\in X:\xi(x,y) = 0\}$. For any set $b\in\mathcal B(X)$ we ...
3
votes
0answers
136 views

Fixed point: general case

This is the second part of the question Fixed point: linear operators. Here I would like to ask you about the general case. A lot of concepts can be described or even defined as a solution of a ...
6
votes
1answer
122 views

Dixon's Theorem to probabilistically bound largest factor of N

I have recently decided to read up on the current integer factorization algorithms. When looking into some of the algorithms, I came across the following statement: Say that p is the smallest ...
4
votes
2answers
350 views

Any idea about N-topological spaces?

In Bitopological spaces, Proc. London Math. Soc. (3) 13 (1963) 71–89 MR0143169, J.C. Kelly introduced the idea of bitopological spaces. Is there any paper concerning the generalization ...
2
votes
0answers
89 views

Norm on a module over an ordered ring

The definition of norm defined satisfies positive homogenity, triangle inequality, and separation of points. Now, suppose, I have a module $M$ over an ordered ring $R$ where $R$ is endowed with an ...
5
votes
4answers
338 views

Reference for Quantum groups

I would like to know if there are any general references that you would suggest to learn about quantum groups? I have looked at some of the "standard" books, but I am wondering if someone is ...
3
votes
1answer
232 views

What is Space Time code? Is there any good book/thesis to understand the subject?

I am interested to learn Space Time code. Is there any understandable books/ lecture notes/ thesis for beginners?
6
votes
1answer
166 views

Gowers norm - gap between $U_3$ and $U_4$ norms?

For a function $f$, it is known that $|f|_{U_2} \le |f|_{U_3} \le |f|_{U_4} \le\dots$ Is there an example for a function $f$ such that $|f|_{U_3} < |f|_{U_4}$ (i.e. they are not equal?). The ...
4
votes
1answer
536 views

Reference request for the following proof of Euclid's Lemma

I'm looking for a reference containing the following proof of Euclid's Lemma. Recall the statement: Let $a,b$ be positive integers and let $p$ be a prime dividing $ab$. Then $p$ divides $a$ or $b$. ...
62
votes
5answers
2k views

Defining a manifold without reference to the reals

The standard definition I've seen for a manifold is basically that it's something that's locally the same as $\mathbb{R}^n$, without the metric structure normally associated with $\mathbb{R}^n$. ...
6
votes
0answers
172 views

non-orientable 4-manifolds

Most of the books and texts I read about classfication problems surrounding 4-manifolds which are closed and orientable (with a occasional side-track to open orientable 4-manifolds). This is ...
4
votes
2answers
113 views

Reference for a certain notion of holonomy

I am reading a paper that says $L$ is a flat complex $G$-line bundle over $M$ with holonomy $\alpha$. Here $G$ is an abelian Lie group and $\alpha$ is a character of $G$. I have two questions: If ...
4
votes
1answer
198 views

Proof of Moisezon Theorem

We call a compact complex manifold Moisezon manifold, if its dimension coincides with the algebraic dimension, i.e. it has as many algebraically independent meromorphical functions as its complex ...
4
votes
1answer
118 views

Reference request: coding in dynamical systems

One of my professors mentioned that a standard problem in dynamical systems is to show that if two points in your system have the same coding (ie end up in specific regions of the space you're working ...
6
votes
5answers
461 views

Mathematician (non-logician) seeks reference for Gödel's incompleteness theorems

I would like to learn more about the proofs of Gödel's incompleteness theorems. I have read and am rereading Gödel's proof by Nagel, Newman, and Hofstadter. I like it very much, but I would like ...
4
votes
2answers
355 views

Measure of Image of Linear Map

I am trying to work my way through the proof of the change of variables theorem for Lebesgue integrals. A key lemma in this context is as follows: If $T:\mathbb{R}^n \rightarrow \mathbb{R}^n$ is a ...
6
votes
2answers
482 views

Reference request: Introduction to mathematical theory of Regularization

I asked the question "Are there books on Regularization at an Introductory level?" at physics.SE. I was informed that "there is (...) a mathematical theory of regularization (Cesàro, Borel, ...
3
votes
2answers
138 views

Looking books about the topology of n-manifold ($n > 4$)

There are a lot of books dealing with the strangeness of the topology of 4-dimensional topology. I wonder if there are books or overview references on the topology of n-manifolds (where n > 4) ? ...
6
votes
4answers
4k views

A good book on Statistical Inference?

Anyone can suggest me one or more good books on Statistical Inference (estimators, UMVU estimators, hypotesis testing, UMP test, interval estimators, ANOVA one-way and two-way...) based on rigorous ...
3
votes
1answer
137 views

Looking for an article on general principles of discrete mathematics

In his article 2 cultures Timothy Gowers states that the structure in combinatorics is there in the form of somewhat vague general statements that allow proofs to be condensed in the mind, and ...
0
votes
1answer
95 views

abide law — how to say and generalization

Suppose that some algebraic operations $+$ and $\oplus$ satisfy the abide law, i.e. $(a_0+a_1)\oplus(b_0+b_1)=(a_0\oplus b_0)+(a_1\oplus b_1)$. How should I say this, “$+$ abides by $\oplus$” or ...
3
votes
1answer
173 views

Anyone knows the name of the Hungarian undergraduate Math Seminars book?

I had this book bookmarked somewhere and now I have lost it somewhere. The only faint description I can remember was something about a culture of Seminars in Hungary and it was decided that a series ...
7
votes
2answers
638 views

Approximating roots of the truncated Taylor series of $\exp$ by values of the Lambert W function

To everyone: don't bother writing up another answer, i'm giving this bounty Antonio's answer. It just doesn't let me yet (24 hours delay). If you map the nth roots of unity $z$ with the function ...
7
votes
6answers
4k views

A Math function that draws water droplet shape?

I just need a quick reference. What is the function for this kind of shape? Thanks.
6
votes
1answer
2k views

Basic facts about ultrafilters and convergence of a sequence along an ultrafilter

Could you help, please. I need the information about the ultrafilters, namely, any ideas how one can see that they exist and a proof of the fact that for any ultrafilter every sequence on a compact ...